Finite Group DatabasebetaFinite Group Databasebeta| order | 6250 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C54 · Schur multiplier (H2) = C55 |
| direct product | C2×H(5,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | C54 |
| commutator, Frattini | C5 | C2×C54 |
| LCS | G ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C2×C5 ◁ G | |
2866 conjugacy classes of subgroups.
1258 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6250, 75);